Starting with

$\displaystyle a= \frac {v_c-100}t$

and

$\displaystyle a = \frac {40-v_c} {2-t}$

set them equal, cross-multiply, and manipulate to get $\displaystyle v_c$ by itself:

$\displaystyle \frac {v_c-100} t = \frac {v_c-40}{2-t}\\v_ct - 40 t = (v_c-100)(2-t)\\v_c(2t-2)=-200+40t\\v_c=\frac {200+140t}{2t-2} = \frac {100+70t}{t-1}$